Ratio and Proportion - Shortcuts & Tricks for Placement Tests, Job Interviews & Exams

welcome to a quantitative aptitude video on ratio and proportion from career.com ratio and proportion is a fundamental topic like percentage and is widely needed in other topics of quantitative aptitude so always four to five questions are generally asked by all placement test job interviews Bank MBA and other exams in various formats on ratios today we'll see shortcuts and tips to solve sums related to ratio and proportion very quickly questions are available on Career right.com where you can practice with thousand plus aptitude questions and practice test so now let's [Music] start let us first understand what exactly is the meaning of ratio and proportion Whenever there are two quantities or more quantities and whenever we are comparing them then their comparison is expressed in the form of ratios okay so let us assume there are two people p and Q and P is five times faster than Q so what does that mean if Q is running at the speed of 10 km/ hour then P would run at the speed of 5 times more that is 50 km/ hour so when we are comparing the speeds of p and and Q what we'll say is that speed what the ratio of speed of p and Q is given by what it would be simply given by the speed of p is 50 and the speed of Q is 10 that would be equal to 5 is to 1 so ratio of speed of p is to Q is 5 is 1 this is the ratio now these are the actual values and when we simplify it and reduce this we get 5 is to 1 because we'll divide by 10 we'll get 10 5 are 50 and 10 1's are 10 so ratio of speed of p is to Q is equal to 5 is to 1 so this is read as nothing but p is 2 Q right now over here this ratio is always ratios are always written like this but there's another way of writing ratio and that is nothing but 5 upon 1 so If the ratio is a is to B you can write it as a by B If the ratio is B is to a you can write it as B Upon A B divided by a this is actually the meaning of ratio it is nothing but when we are comparing two quantities we write their comparison in this format in the format of ratio so ratio can be considered as like a simple fraction okay like say if we say what is the ratio of income of Ramesh is to Sur right say it is uh the ratio is say 2 is to 3 that means that Sur is uh whatever is the income of say rames say it is assume 4,000 rupees then income of sures would be this divided by 2 into 3 6,000 rupees because when we reduce this we'll get 2 is to 3 as the ratio remember these are not the actual values this is nothing but a ratio the simplified form of the actual values right again when we solve some sums we will realize what exactly we mean by ratio how we take ratio how to use ratio for solving the sums or given numericals right now what is the meaning of proportion whenever we compare two ratios or equate two ratios we call it as proportion so if say we have two ratios a is to B and C is to D and when we equate these two okay A to B can be written as a upon b c to D can be written as C upon D when we equate these two ratios we call it proportion okay and whenever we write a upon b as a is to B and C is to D in this format instead of using the is equal to sign what we write we write these four dots and we read it as a is to B as C is to D okay these four dots mean as a is to B B likewise as C is to D like what does that mean just like C is to D is there a is to B is there okay this is nothing but proportion that is when we equate two ratios it is called as proportion now before moving on to sums let us take a look at some shortcuts or tips related to ratio and proportion which would be very very useful to solve not only sums related to ratio and proportion but also other topics of quantitative Act aptitude where you'll encounter ratios so right now we'll check out the tips first the first step over here is pretty easy let us assume there are two ratios a upon B and C upon D and they are proportional that is they are equal then simply a * D would be equal to B * c a d we just cross multiply right now let us see the second tip let let there be two ratios okay a by B and C by D now they might be proportional they might not be proportional okay so let's not write the equal to sign right now we have to see which fraction is greater which ratio is greater how to do that very easy take this a take this D and multiply them what you'll get a d okay take this B take this C multiply them that is nothing but we are cross multiplying just like we did over here okay now if ad is greater than BC that means left hand side is greater than right hand side so left hand side ratio must be greater than right hand side ratio so we will have AB greater than C upon D if a is less than BC that means right hand side ratio is greater than left hand side that means left hand side is smaller so left hand side a by B is smaller than right hand side that is C by D correct and if a is equal to BC we already know both must be equal right see how easy it is let's move on to the next tip okay now if there are two ratios a upon B and C upon D and they are proportional that is they're equal then we can simply write a upon B is equal to C upon D therefore A + B upon B would be equal to C + D upon D denominator remains common what do we do to the numerator we are just adding the denominator if on the left hand side we add the denominator on the right hand side also we have to do the same thing and we'll get it as same okay this is known as compono right this is the component rule of ratio and proportion now what we did was we added the denominator right now what we can say is a upon B = to C upon D this is a upon Bal to C upon D when we added we got it as equal so we'll now subtract upon B would be equal to C - D upon D this is also true this is known as dividendo okay division or dividendo compono is addition dividendo is subtraction now again let's take a look at another tip if we divide this and this what you will get you'll get a + b upon B / a - b upon B would be equal to C + D upon D / C minus D upon D everything gets cancelled and what do we get over here A + B upon a - b would be equal to C + D upon c - D this is known as compono dividendo we can rewrite it as this if a upon B is equal to C upon D then simply a + b Upon A minus B will always be equal to C + D upon cus D this is the compono dividendo rule for ratio and proportion remember this this is also important in exam they can simply ask you give you a value of a b c and d and they can ask you what is the value of a + b Upon A minus Bal to C plus d upon C minus D and all that stuff so remember this tip okay the next tip okay that we are going to see is again very very easy the sixth one is if we have a upon b = c upon D then what we can say is inverse is also true that means B Upon A will be equal to D upon C we simply inverted d a upon B we inverted to B Upon A C upon D we inverted to D upon C it is true this is known as invert Endo there's no need to remember the names actually but this is just for information sake right if a upon B is equal to C upon D then B Upon A is equal to D upon C exactly inverted that is invert now moving on to the seventh tip okay say we have a ratio of three numbers like a is to B is to C this is known as the first proportional this is the second proportional and this is the third proportional right now this and this are at the end right this is at the start at the end so these are nothing but extremes right these are nothing but extremes and this is the center so this is the mean so these are extreme proportionals this is mean proportional right and if there are say what we can say say there are four ratios then what we'll say this is the first proportional this is the second proportional this is the third proportional this is the fourth proportional the these two are extremes and these two are means okay these two are extremes and these two are means right so a is to B is to C this can always be written as a is to B and B is to C and both are proportional okay a is to B is to C is to D can be written as actually there are four dots over here a is to B is as C is to D okay this this can be written as a is to B same as C is to D it can be written as a upon b = c upon d right so a is to B is to C is to D can be written as a is to B same as C is to D that can be written as a upon b equal to C upon d right now this is the seventh tip now let us see another very very useful tip okay that would be useful to solve all the sums whenever we have a ratio say a upon b or let us take some number 5 upon 6 okay or we can write it as 5 is to 6 now these are not the actual values what are these These are nothing but the simplified values so so take a example if we have actual values of 40 and 48 okay then the ratio on simplifying that is on dividing by 8 what you'll get 8 5 are 40 8 6 are 48 and we get the ratio as 5 is to 6 that means these are nothing but ratio values these are not the actual values so how to find actual values from the ratio values very easy let us assume the common factor as K and the actual values would be 5 into the common factor 5 K 6 into the common factor as 6 K over here what is the common factor for 40 and 48 it is nothing but 8 when we divide by this common factor you'll get the ratio 5x 6 so if you multiply 5x 6 by this common factor we'll get the actual values 58 are 40 and 68 are 48 same way in exam or in sums we do not know exactly the common factor so let us assume the common factor to be K so the actual values will be 5 into K 5 K 6 into K 6 K right we'll be using this in later on sums and this would become clearer and clearer how this is useful to solve the sums right but just remember always take common factor K and then get the actual values now let's move on to question number one which of the following two ratios is greater 17 is to 18 and 10 is to 11 what have we seen we have two ratios 17 by 18 and 10 by 11 what should we do take 17 take 11 multiply them take 18 take 10 multiply them what do we get 17 10 17087 180 187 is greater than 180 left hand side is greater than right hand side so left hand side ratio must be greater than right hand side ratio so 17 by 18 is greater than 10 by 11 see how easy it was now this is for two ratios only let us assume that they have given you say three ratios like say 4X 5 2x 3 and 1X 2 compare these three and find out which is the greatest okay what you'll do you'll take these two okay and find the greatest whatever will be the value we'll compare that and this and find the greatest and that would be your answer very easy if they are giving you four ratios 1 2 three and four there are four ratios compare these two compare these two you'll get two answers right whichever is the greater okay out of these two you'll get the greater one out of these two you'll get the greater one compare these two you'll get the greatest among all the four same is the technique for smallest if they would have asked which is the smallest one what we would have said right hand side is smaller than left hand side so right hand side equation must be smaller than left hand side equation so 10 upon 11 is smallest okay if they would have asked smallest but here they have asked greatest so 17 by 18 is greatest see how easy it is moving to question number two the third proportional to 18 and 54 is now what have we learned over here a is to B is to C this will be the first proportional this would be the second proportional and this would be the third proportional right so we have to find the third proportional this can also be written as a is to B as a is to B as C is to D okay or B is to C right B is to C that is a upon B is proportional to B upon C so b² would be equal to AC we know we have two values that is a is 18 B is 54 and we have to find the third proportional so we'll have 54 squ that is 54 into 54 equal to 18 into C 183 are C is 162 now this is the third proportional sometimes they might ask you to find what is the mean proportional now in a is to B is to C the mean proportional is the second one right that is we have to find the value of B and we already know this can be written as a upon Bal to B upon C and that is nothing but b² equal to AC so you can get the value of mean proportional also moving to question number three what is the fourth proportional in 913 and 153 so we have a we have B we have C and we have D because we want the fourth proportional and what do we do we have is to B B is to C and C is to D then only we can say this is the first proportional this is the second proportional this is the third proportional this is the fourth proportional and this is what we have to find we know that value of a is 19 this is 13 this is 153 and this we have to find now this can be written as a is to B as C is to D this is nothing but a upon b equal to C upon d right we have to find the fourth proportional that is D what is D BC upon a right so let us solve value of D would be how much B is 13 into 153 divided 9 9 1's are 63 17 are 17 into 10 is 170 17 into 3 is 51 so uh 170 + 51 is 221 the value of D or the fourth proportional is 221 moving to question number four find the mean proportional between 7 and 63 like we have seen earlier since they have given 7 they have given 63 and they want the mean proportional that means the third number or the the third number we have two numbers so the third number is needed mean proportional or the mean is always at the center so over here okay in a is to B is to C these are extremes and this is nothing but mean mean so we want the value of B we know this can be written as a is to B as B is to C A upon B would be equal to B upon C okay that means b square is AC and we have to find the value of B we know what is b square this is 7 into 63 that is 7 into 7 into 9 63 7 n are okay so value of B would be taking square root of 7 into 7 into 9 7 and 7 so square root would be 7 multili by square root of 9 would be 3 answer is 21 so the mean proportional is 21 moving to next question question number five 10 upon 13 is equal 11 upon 28 is equal 21 upon 11 isal 12 upon 11 isal K what is K now whenever such some uh such sums come in ratio and proportion please remember they are very very very easy to solve you won't even believe how to how easily we can get the answer and what exactly is the solution let us see how to solve simply add the numerators what do you get + 12 divided by simply add the denominators what do you get you'll get the value of K that would be 10 + 11 is 21 + 21 is 42 + 12 is 54 13 uh 11 + 11 is 22 + 28 is 30 40 50 + 13 is 63 right 96 97 this is the value of K simply add numerators divided by simply add the denominators right and you get the value of K moving to next question question number six income ratio of Ramesh and Sur is 5 is6 their spending ratio is 7 is9 Ramesh saves rupes 4,000 and Sur saves R 3,000 income and spending respectively of rames and Sur are now look over here what have they given income of Sur income ratio of Ramesh and Sur is 5 is6 these are not the actual values this is nothing but ratio this is not the actual values like rupes 4,000 or rupes 3,000 this is just a ratio these are not actual values so how to find actual values we have learned let the common Factor b k so the actual income of rames is how much Rupees 5 into common factor that is 5K actual income of Sur is how much Rupees 6 into the common factor 6K right now what do we know income or the total money is the income is nothing but spending or the expenditure plus the saving whatever we spend spend plus whatever we save that is nothing but the income that is the amount of money which we receive so what is spending spending is income minus saving correct now what is the spending for Ramesh what is the income of Ramesh 5K what is the saving of Ramesh 4,000 right what is the spending of sures what is the income of sures 6K what is the saving of sures 3,000 and they have given spending ratio is 7 is9 that means spending of Ramesh divided by spending of sures is equal to 7 upon 9 so we'll divide this also so what do we get let's write over here 7 by 9 is 5 K - 4,000 / 6 K - 3,000 what will we get 7 6 are 42 K - 21,000 that would be equal to 9 5 are 45 K - 9 4 are 36 36,000 okay so take this 42 over here 36 over here 36 - 21 15,000 would be equal to 3K K would be equal to 5,000 now we got the value of the common factor so what is the income of rames now 5 into 5 25,000 what is the income of Sur 6 into 5 30,000 now we have to find the spending Ramesh saves 4,000 rupees right so what is spending income minus 4,000 that is 21,000 is spending of rames then 30,000 Sur says 3,000 rest is spent so 30,000 minus 3,000 is 27,000 is the spending of sures see how easy it was you just need to remember for take to calculate actual values just take the common factor as K and then we just need to equate and solve it moving to question number 7 a is to B is 3 is 7 and B is to C is 9 is 5 what is a is to B is to C now we cannot directly write three uh we have a is to B and we have B is to C what is here 3 is to 7 what is here 9 is to 5 now we have to find a is to B is to C so we cannot directly write value of a three value of C is five because here B which is there there is only one B over here but there are two B's over here and value of both are not same so what to do very easy just make the values of both the bees same and then we can write the answer okay how to make the values of both the bees same First Take This ratio what is it three is to 7 now what are the two values of B 7 and 9 we have S over here correct so multiply by 9 what you'll get throughout 3 into 9 7 into 9 correct now take this second ratio what is it 9 is to 5 now what are two values of B 7 and 9 but we already have 9 over here so take this seven and multiply throughout 9 into 7 5 into 7 what do you get 9 3 are 27 7 7 9 are 63 9 7 are 63 5 7 are 35 now we have the values of b as same correct so we can write this is A's value this is C's value so a is to B is to C is nothing but 27 is 63 is to 35 see how easy it was you just have to make the values of B common or same how we how did we do just multiply by the other value okay and here just multiply by the first value of B and we get the same values this is like calculating C LCM or finding the LCM of 7 and 9 okay now moving to next question how to divide 3395 in ratio of 42 is 32 is 23 now this is very easy sum and there are two ways to solve this sum one way we have already seen in the partnership video if not please check out the partnership video okay this is very important where we learned how to find the share of profit what we did there was say three people having the share of profit of pqr are three people and they are having the share of profit of 42 32 and 23 okay then how to find the share of P or Q or R okay so we'll solve by both methods the first one is the share or the partnership method which we have seen how to divide 3395 ratio 42 32 and 23 very easy the first part would be 42 upon 42 + 32 + 23 multiplied by the total that is 3395 of whose we want to find the parts what you'll get 42 upon 97 * 3395 actually 97 into 35 is 3395 I'm not showing calculation over here I'm just showing you the method so that we found out to be 147 0 second method or the second part is what is the ratio for the second part 32 32 divided 42 + 32 + 23 that is all the three parts multiplied by 3395 the total what do we get 32 into 35 right that would be equal to 112 0 now the third part you can find by this method or what you can do is you can add both of the these and subtract from 3395 okay let's add them what do we get on addition we get 09 5 2 and we have to subtract it from what we have to subtract it from 3 3 9 and 5 what do we get 5 0 13 - 5 8 2 - 2 is 0 so 8 05 is the third part right so we got the three parts this is how you divide 3395 into three parts okay so that the ratio is 42 is to 32 to 23 now let's move to the second method using the techniques which we have seen right now here it is the ratio it is not the actual value you have to find the actual value so how to find the actual value let us assume the common factor to be K so the actual values are 42k 32 K and 23 K okay now these are the actual values what does this mean these are the three parts of 33 95 that means when we add these three parts we get 3 395 what do we get + 32 k + 23 K would be equal to 3395 97 K would be equal to 3395 K would be equal to 35 what is the first part 42 K 42 into 35 that would be 1470 second part again the same way over here what do we get second part is 20 uh 32k 32k is 32 into 35 that is 1120 and the fourth part is again you can add and subtract or you can have it as 23k that would be equal to 23 into 35 is 85 so these are the three parts any method you can go by it's your choice go by the method where you feel you are comfortable and calculate very fast okay moving to question number nine 285 is summation of three numbers ratio between second and third numbers is 6 is5 ratio between first and second numbers is 3 is 7 the third number is again very very easy sum let us see how to solve it ratio between the first and the second number is what 3 is 7 ratio between second and third number is what 6 is 5 we have second over here we have second over here right I'll write it over here so it would be become easier to compare okay but the values of both are not same so what to do just make the value same so once we make the value same we'll get it in the format this and then once you have in this format this is the first number this is the second number this is the third number we can solve just like the previous sum where the summation is given and we have to find the three parts correct so this sum is the combination of previous sums and the sum number eight which we just saw now let us make the value of second number same how to do it take this three 7 two values are 7 and six we already have 7 multip by 6 multiplied by 6 you'll have 6 3 are 18 7 6 are 42 take this 6 5 two values of two are 7 and six we already have six so multiply by 7even throughout what do we get we get 42 is to 7 5 are 35 so values of the second number are now same so the first number is to second number is to third number is nothing but 18 is to 42 is to 35 right we have to find the third number okay third number ratio is this so what is the third number 35 upon 18 + 42 that would be nothing but 50 60 95 right + 35 is 95 multiplied by what is the addition of the all these three 285 so total of all the three numbers is 285 right so what do we get 95 into 3 35 into 3 is 105 3 39 15 yes 105 so the third number is 105 see how easy it was moving to question number 10 ratio of two numbers is 3 is to8 on adding five to both numbers the ratio becomes 2 is to 5 which is the smaller number out of the two now the ratio of let the two numbers Be A and B okay the ratio of two numbers is 3 is to 8 and they are saying that these are not the actual numbers this is nothing but the ratio they say that on adding five to both numbers okay ratio becomes 2 is to 5 that means five is added to the numbers it is not added to the ratio right so what are the actual numbers if this is the IO let the common factor be K so the actual numbers are 3K and 8 K now what they say on adding five to both numbers add five to both numbers 3 k + 5 8 k + 5 the ratio becomes 2 by 5 that means ratio of the first number to second number becomes 2 upon 5 let us solve what do we get 15 k + 25 = 16 k + 10 that would be equal 25 - 10 is 15 15 = to 15 = to K value of K is 15 smaller number 3K and 8 k k k is same so the smaller number is three out okay so smallest number or smaller number out of the two is 3 K 3 into 15 is 45 smaller number is 45 moving to question number 11 find a is to B is to C is to D when a is to B is 2 is 3 B is C is equal to 7 is 9 C is to D = 5 5 is to 9 now now here lies a problem okay what have we learned up till now if it is a is to B is to C that means if it is a is to B and B is to C and if there are two different values of B we can simply make the values common and then we can write a is to B is to C but over here there are two different values for B there are two different values for C and it is not just a is to B is to C it is a b c and d so how to solve such a sum because if we try to make the value of say C same then value of B will also change and if we try to make value of B same value of C will also change so how to solve such kind of sums very easy there's a trick to it okay first I'll explain you the trick okay by solving the sum then I'll explain you the generalistic formula right now first what you need to do is you know a is to B is 2 is to 3 right 2 upon 3 over here next B is to C what is it 7 upon 9 next C is to what is it 5 upon 7 now equate all of them okay now what we want value of a is to B is to C is to D that is we want four values over here right but we already have six values so how to calculate these four values very easy this is the first value and this is the last value how to calculate first and last first is by multiplying the numerators 2 * 7 * by 5 what do we get 2 4S are uh 2 into 10 2 5 are 10 10 into 7 is 70 first value is 70 just multiply numerator what is the last value just multiply the denominator exactly opposite right 3 into 9 into 7 9 7 are 63 63 into 3 is 189 okay so we got the first and last value okay very easy now how to calculate these middle value vales very easy this is the second number which we want so which is the second number in this this is first this this is first second third fourth fifth and sixth this is the second number so start from here from here just go to the third number because three comes after two and here from here just jump directly to five parallel so go from three from two you should go to the third number and directly to the five right parallel number so 3 into 7 and multiply all these 3 7 are 21 21 into 5 is 1 05 this is the second number now how to find the third number very easy again start with second only now here you jump to third go opposite here you jump to the fourth then after fourth what what did you do after three you jumped to the fifth number here also jump to the fifth number so multiply 3 into 9 is 27 27 into 5 or 15 3 are 3 into 5 is 15 15 into 9 is 135 this is the answer see what we did we did this we did this then we did this then we did this very easy just remember this diagram okay what is the diagram say it is a upon b c upon d e upon F do this do this do do this and do this okay very easy you don't need to consider anything this middle diagram which is there it is like a rhombus okay or like a square or something like that two different arrows okay you just remember just go like this if you remember this diagram you'll be easily be able to remember the entire formula because there is nothing to it see go here and go here then go here straight then again meet over here here right like a kite this is like a kite you have to make a kite how let's practice the diagram again first second okay first and the last how to find the second start from the bottom go at the middle go over here go straight go over here right so see how easy it is just remember this diagram practice practice the diagram for four to five times your hand will automatically will remember the diagram and you'll even if if you don't know the formula you'll in exam automatically your hand will draw this diagram like this and you'll be able to remember the formula right this is the first term this is the last term that is the fourth one this is the second term and this is the third term now let us see what is the generalistic formula if a is to B is small a is to small B if B is to C is small C is to small d D and if C is to D is Small E is to small F then value of a is to B is to C is to D is given by very very very easy thing what we'll have a c and d this is the first value last value is BDF right now what is the second value over here take the second one okay b c and e the third one would be b d and e okay so you have a upon B = to C upon D equal to e upon F take this take this take this and take this you get a kite over here okay see how easy it is just remember the diagram you'll be able to solve the question okay moving to question number 12 question number 12 price of each article of type P Q and R is rupes 300 rupees 180 and rupes 120 respectively Sur buys articles of each type in the ratio 3 is to 2 is to3 in rupes 6480 how many articles of type Q did he purchase again extremely easy sum let us understand what they're saying Sur in total spends How much rupees 6480 on what he buys articles of three types okay of P of Q and R type P article rate is rupees 300 per article for Q it is rupees 180 per article for R it is rupees 120 per article of type PQ and R how many articles did he buy we do not know we only know that the ratio of the quantity of articles that is of p is to Q is to R quantity is what of type P is to Q is R is 3 is 2 is to 3 do we know the actual value or the actual quantities no so how to find actual values let the common factor be ke be K so the number of Articles of type P that Sur bought was 3 into K of type Q it is 2 into K and of Type R it is 3 into K okay so of type P Sur bought 3K articles of type Q he bought 2K articles of Type R he bought 3K articles so total amount of money spent by sures for type P is one article is 300 rupees total articles are 3K of type P so total money spent for type P is 900k total money spent for type Q 180 rupees per article out of that he bought 2K articles right uh that 180 rupees price rate is of one article total artic bought are 2K so that would be 360k same way 120 rupees for one article so 3K articles cost 360k rupees and this total expenditure is nothing but 6480 because he spends this much so 64 6480 would be equal to how much 1620 okay K this gets cancelled 2 8 are 81 2 into 3 2 4 81 into 4 so value of K is 4 so number of Articles of type Q are nothing but 2 K that is 2 into 4 is 8 so Sur bought eight articles of type Q moving to next question question number 30 Ajay and Raj together have rupes 1050 on taking rupees 150 from Ajay Ajay will have same amount as what Raj had earlier find the ratio of amounts with a a and Raj initially now we do not know the ratio we do not know the initial amounts anything but let us assume that aay has a rupees Raj has R rupees initially okay now we know that together they have 1050 so a plus r would be 1050 rupees right now what they say when we take 150 rupees from AJ so AJ minus 150 rupees then Ajay will have how much amount it would be as what Raj had earlier Raj had R rupees earlier so it would be R so that is nothing but a minus r is 150 this is first equation this is second equation just add them what do we get a + r + a - R = 150 + 1 52 a would be equal to 1200 a would be equal to 600 if a is 600 how much will R have that is Raj have one a + r would be equal to 1050 put the value of a r will be 1050 - 600 450 rupees okay so what is the ratio of amount of Ajay and Raj it would be 600 is to 450 now divide by 15 what you'll get 4 40 okay is to 30 that would be 4 is 3 so ratio of amounts with a and Raj initi I is 4 is 3 moving to next question question number 14 if x is to Y is equal to 3 is 4 then 7 x + 3 Y is to 7X - 3 Y is equal to again extremely easy sum and there are two ways to solve these sum this sum okay let us see both the ways first way is the best shortcut method okay let us see what the shortcut is whenever they have given X is to Y is 3x 4 okay and then they give such a find the value of this and all that stuff simply put what we have X upon Y is given as 3x 4 so put the value of x as 3 put the value of y is 4 what you'll get x + 3 y upon 7 x - 3 y we have to find the value of this so x value is 3 7 3 is are 21 3 4 are 12 7 3 is are 21 - 12 that would be how much 33 upon 9 11 upon 3 we got got the answer now let us see what is the second method okay second method is actually also easy but I would prefer go with the shortcut method but I'll teach you the second method also why because sometimes it might be useful or this thinking pattern is also useful if you see over here what do you have X and Y and here you have x + y and x - y so this is the component dividendo format what do you have over here x upon Y is 3 upon 4 but over here you do not have simply x + y and x - y here you have 7 x + 3 y 7 x - 3 y so let us try to get in that format first we want 7x so multiply by 7 multiply and divide by 7 on the left hand side or multiply by 7 throughout what you will get 7 x upon y would be equal to 7 3 are 21 upon 4 correct multip by 7 over here multiply by 7 over here now multiply now divide by 3 on both sides what you will get 7 x / 3 it would become 3 y 21 divided 3 it would be 3 4 are 12 you got 7 x you got 3 y now apply component dividend what it is if a upon B is equal to C upon D then a + b Upon A minus B would be = C + D upon c - D so 7 x + 3 y upon 7 x - 3 y would be equal to 21 + 12 21 - 12 that is nothing but 33 upon 9 just like previous we got the answer 11 by 3 moving to question number 15 if a is to B is equal to 5 is 7 and C is to D is equal to 2 a is to 3 B then AC is to BD is again very easy what have they given a upon B is 5 upon 7 and C upon D is equal to 2 a upon 3B this is our first equation this is our second equation multiply equation 1 and 2 what do we get a upon B * C upon D would be equal to 5 upon 7 * 2 a upon 3 B AC upon BD okay would be equal to we know what is this 5 2 are 10 10 a upon 7 3 are 21 21 B what is the value of a upon B 5 by 7 10 upon 21 into 5 by 7 it is 50 upon 21 into 7 is 74 50 upon 147 so AC is to BD is equal to 50 is to 147 moving on the three numbers are in the ratio 1X 2 is to 2x 3 is to 3x 4 the difference between greatest and smallest numbers is 36 find the numbers now the ratio of three numbers is 1x 2 is 2x 3 is to 3 by 4 we do not know the actual numbers this is nothing but ratio so what would be the actual numbers how to find the actual numbers let the common factor be K so the actual numbers are K by 2 2x 3 into K is 2 K by 3 3x 4 into K is 3 K by 4 now we have to find which is the greatest and smallest in this it is very easy let us see K by2 is nothing but 1 by 2 that is. 5 K second one is 2x3 that is nothing but 666 K and third one is 3x 4 K that is nothing but 75 K so this is the greatest this is the smallest difference between greatest and smallest they have given so 3 K upon 4 minus K upon 2 is equal 36 right multiply by 4 throughout what you'll get over here you'll have 3 K minus 4K / 2 that is 2K would be equal to 36 into 4 right so value of K would be 36 into 4 right what we have to find out we have to find out the numbers what is the first number K by 2 that is 36 into 4 / 2 that is uh 36 into 2 72 right second number is 2K upon 3 that would be 2 into K is 36 into 4 ided by 3 12's are okay 12 into 4 is 48 48 into 2 is 96 right third number it is let's find out over here at the bottom 3K by 4 that would be 3 into 36 into 4 / 4 36 into 3 is 144 so 36 into 3 is 108 sorry 108 so the three numbers are 72 96 and 108 okay instead of calculating the third number this way you can also calculate it by this equation that is difference between the largest and the first number that is smallest is 36 so you can add 36 to 72 and you'll get 108 moving to question number 17 the ratio of market prices of Wheat and Patty is 2 is to3 and the ratio of quantities consumed in a family is 5 is to4 find the ratio of expenditure of Wheat and Patty here we do not know actual values we know only the ratio so price of wheat is to price of pad is how much 2 is to 3 the ratio is 2 is 3 so what are the actual values let the common factor be K actual values are 2K rupes and 3K rupes this is for wheat and this is for Patty okay this price is for Patty this price is for wheat now ratio of quantities consumed so how much is the wheat consumed okay how much is the wheat consumed and how much is the pad consumed it is 5 is 4 again this is not the actual values we have to find the actual values this is nothing but the ratio but since we took Factor K over here we cannot repeat the same factor over here because we do not know if the factors are same so let us take another Factor say a so actual quantity of wheat which is consumed is 5 into a is 5 a actual quantity of PTY which is consumed is 4 into a is 4 a now what is the expenditure for wheat it is nothing but rate for wheat that is price for wheat multiplied by the quantity consumed okay quantity consumed right same way expenditure for the pad would be a rate for pad right multiplied by the quantity consumed is that right and we have to find the ratio of expenditure of Wheat and Pad so we'll divide this also what is the rate rate for wheat is 2K multiplied what is the quantity of weat consumed 5 a divided by what is the rate for pad 3 K multiplied by quantity consumed is 4 a this gets cancelled what do we get 10 upon 12 that would be 5 upon 6 so the expenditure of we ratio of expenditure of v10 pad is 5 upon 6 there is another way see over here the factors got canceled out over here right KK gets canceled a a gets canceled so what you can do is you can write expenditure is nothing but rate into quantity consumed so expenditure for we upon expenditure for p is nothing but what is the ratio for the rate 2x3 multiplied by what is the ratio for quantity ratio of expenditure is nothing but ratio of quantity multiplied by ratio ratio of rate multiplied by ratio of quantity so ratio of expenditure of we to P is ratio of rate of 2x3 and the other ratio is 5 upon 4 you'll get the same answer 10 by 12 equal to 5 upon 6 okay but if you are getting confused with this you can use our simple method and calculate moving to question number 18 Rupees 8,400 is divided among a b c and d in such a way that shares of A and B B and C and C and D are in ratios 2 is 3 4 is to 5 and 6 is 7 respectively share of a is now what have they given share of a is to B is 2 is to 3 B is to C is 4 is to 5 and C is to D is 6 is to 7 now share of a generally if we have a is to B is to C is to D we can very easily calculate the share of a but do we have this no we do not have this we have these three values now if you see this looks very similar to a sum which we solved earlier what was the sum and what was the formula for getting a is to B is to C is to D this this go like this go like this okay and get a kite over here right so what do we have a is to B is 2x 3 B to C is 4X 5 C is to D is 6 by 7 and we simply equate them right the three four so these are the four values of a b b c and d okay how to get a is to B is to C is to D take this first 2 4 are 8 8 into 6 is 48 how to get the last value take this 3 5 are 15 15 7 are 105 how to get the second value start with second go like this and take this 3 4 are 12 12 6 are 72 how to get the third value simply go straight then go up 3 5 are 15 15 6 are 90 so this is a is to B is to C is to D now what will be share of a very easily by the partnership type or the partnership uh in the video we have seen how to find share of 1 person we have also seen in previous sums share of a is nothing but what is the ratio for a 48 divided by 48 + 72 + 90 + 105 multiplied by total value what is the total value or total amount 8,000 , 400 what you will get over here 48 into 8,400 divided 72 + 8 is 80 80 120 120 + 90 is 210 and this is 35 okay 3155 is over here so let us calculate what the value might be you'll have 15 2 are 1's are 15 5 are 75 90 15 6 are 90 500 60 over here now we have we this 3 into 16 3 into 7 7 8 are 80 are so we'll have 16 into 80 that would be 16 into 8 160 minus 32 that would be 1 8 6 are 48 128 1 28 0 Rupees is the share of a see how easy it was moving to question number 19 in a library the ratio of number of story books to that of non-story books was 4 is3 and total number of story books was 1 2 48 when some more story books were bought the ratio became 5 is to3 find the number of story books bought now very easy what have they given ratio of number of story books to that of non story books was 4 is to3 that is 4 upon three and total number of story books was 1 2 48 so we have 1 2 48 upon non story books would be equal to 4 upon 3 so the number of non-story books would be 3 upon 4 into 1 2 4 8 okay that would give us 936 this is the number of non-story books now in second case some more story books were bought so non-story books will remain same it won't change okay now some more story books were bought right let us assume that M number of story books were bought so what is the number of story books now it would be 1 2 48 that is the previous amount plus M this is the new number of story books and they have given the ratio became 5 is to three that is the ratio of story books to the ratio of non-story books became 5 upon 3 number of story books are now 14 12 48 + m divided by 936 why because that is the number of non-story books that would be 5 upon 3 so what do we get on solving we'll have 3 into 1 2 48 + m would be equal to 5 into 936 we'll get the value of M as 32 so this is nothing but the number of story books that were added or bought later on see how easy ratio and proportion was if you know the basic concept and if you just know uh what the Small Tricks of uh finding the actual value by assuming the factor as K you can very easily solv related to ra solve sums related to ratio and proportion and you can use it in other topics of quantitative aptitude also with this we come to the end of tutorial on ratio and proportion if you like this video please give it a like and share it with your friends give your comments and suggestions below you can also mention topics on which you want videos for us to develop we would be rolling out most such videos and tutorials so subscribe to our Channel and stay updated